They urged all separated parents to see the “bigger picture” and consider the harm that legal disputes cause children. Lord Justice McFarlane said mothers and fathers had “a responsibility and a duty” to help children maintain contact with the other parent.

The Government has announced plans to reform the law to enable fathers to see their children. The changes would to spell out the right of children to have a “meaningful relationship” with both parents after a separation.

The judge was speaking at the conclusion of a legal battle between an unmarried couple who had a six-year relationship. In 2008, the mother left home without warning, taking her daughters, who were then aged four and one, and refusing to let the father see them.

She accused the father of abusive behaviour, but nine of the 10 allegations were unproven. At one court hearing, he admitted spitting at the mother on one occasion. A district judge who heard the case in 2009 noted that the father was a “forceful character” whom the mother found difficult to resist.

In February this year, the father, from the Swindon area, was banned by a family judge from having any direct contact with his children, now nine and six. The father was told he could send his daughters cards, letters and gifts once a month, but could not see them because it would be too distressing for their mother.

The county court judge said that she would be “unable to cope” with the father seeing the children after she broke down in court and said the thought of it made her feel “exhausted”.

The father’s lawyers challenged the judge’s decision, saying it had been based on a “momentary” display of emotion from the mother in the witness box and the views of a “lone” psychologist, who supported her case. The decision also went against the view of the independent advocate appointed for the children.

The father’s barrister, Sarah Evans, told the Court of Appeal: “It is a fundamental tenet of the law of this country that, save in exceptional circumstances, children have a right to a meaningful relationship with both parents.” The appeal judges accepted that the father’s exile from his own children’s lives violated his rights.

Lord Justice McFarlane recognised that it was “a very big ask” for the mother to accept that her children’s best interests lay in having two parents, not just one.

“Where, however, it is plainly in the best interests of a child to spend time with the other parent then, tough or not, part of the responsibility of the parent with care must be the duty and responsibility to deliver what the child needs, hard though that may be,” he said.

The judge, sitting with Lord Justice Rix and Lord Justice Tomlinson, overturned the family judge’s order and directed the mother to “facilitate” contact. The process will take place under the supervision of a court-appointed guardian.